Evidence for the Big Bang and the Expansion of the Universe Part-1 - Completely Remote Sensing, GPS, and GPS Tutorial

Evidence for the Big Bang and the Expansion of the Universe Part-1

What evidence leads to and supports the Big Bang model? A good review of the resulting expansion (and calculated rates) and ages derived from these observations can be found in a Scientific American article (October, 1998; pp. 92-96) prepared by Dr. Wendy L. Freedman.

Two accepted lines of proof for the Big Bang, already described, are restated:

1) The details of the creation physics and progressive emergence of various elementary particles during the first minute of the Big Bang (the Standard Model and its variants; see page page 20-1) are consistent with a model based on Big Bang precepts; these particles are the outcome of a history that can be predicted and explained by Quantum and High Energy Physics, that is, the theoretical production and sequence of particles seems verified by the observed amounts of H, He, and Li atoms in the Universe; and 2) The observations, particularly from HST, of the farthest galaxies as being more primitive in appearance and development - are precisely what is expected from the expansion model in which those parts of space (in which the galaxies are embedded) that have moved the fastest are now the most distant. Thus, we see them in earlier stages of evolution when they were younger as we look back in time outwards from our frame of reference,.

But, even more convincing are two other physical observations that are best explained by a Big Bang origin for the Universe, especially in terms of its expansion behavior: redshifts of light (towards longer wavelengths) from the stars as a composite source in galaxies and cosmic background radiation.

The Hubble Law and the Cosmological Redshift

In the 1920s, Edwin Hubble made revealing observations through optical telescopes. Using Cepheid stars as distance indicators he found that some of these were much farther away than any of those in the Milky Way. He knew the following about Cepheids in the M.W.: 1) they brightened and dimmed in a regular pulsating way, and 2) the higher the frequency of pulsation, the brighter (more luminous) the stars were in their radiation output (since distances to other stars adjacent to the Cepheids were fairly well known [see below], the luminosity of the Cepheids could be deduced). These two plots establish these ideas:

As early as 1924, Hubble had found Cepheids in a great cluster of stars we know as the Andromeda galaxy. When he applied the period-luminosity relationship to these Cepheids, they were notably dimmer (less luminous) than he expected. The most logical conclusion: the host Andromeda galaxy was much farther away (hence, the relative dimming) than any stars in the Milky Way, whose size had been established as about 100000 light years. Thus, the Andromeda collection of stars had to be a galaxy beyond the Milky Way. This deduction is one of the great achievements in Astronomy and all of Science for that matter.

Relying on more Cepheid measurements, by 1929 Hubble had observed various galaxys that were less than a billion light years from Earth but outside the M.W. Here are the data he published then:

Working with others, he extended his observations to even farther distances, publishing this plot in 1931:

Comment: This discovery was worthy of a Nobel Prize. But in those days, Nobels were awarded for Physics but not Astronomy. Hubble championed the cause to change that and after his death, astronomers became eligible for this prize.

Hubble's other great discovery is the now strongly confirmed fact that the velocity of expansion (of the Universe) is directly proportional to its distance from the point of observation (for us, on Earth or in nearby space).

Hubble noted that, as recessional velocities Vr were measured for stellar sources over the range of astronomical distances D that could be measured accurately at that time, the plot of Vr/D disclosed a straight line relation whose slope has a value H, known as the Hubble Constant, named after him. This, the Hubble Law, is the fundamental statement of the Big Bang model. We repeat here his first published plot of velocity versus distance.

From Astronomica.org

The resulting straight line plot is easily described mathematically, in the basic Hubble equation:

Vr (velocity of recession) = H0 x D (distance)

The scale constant is designated by the letter H, and is called the Hubble Constant (stated as H0, which refers to the present day value; H has been different in the past). It is normally given the units of Km/sec/Megaparsec (an alternate form is Km/sec/million light years). The current value for H0 is 71.4 Km/sec/Megaparsec or 21.5 Km/sec/million light years). The uncertainty in the value is about +/- 10%.

The prime information derived from this equation is that objects (such as galaxies) appear to travel at ever increasing velocities as their distance from the observer (Earth) becomes ever greater. The upper limit to expansion rate is the speed of light (although some interpretations of inflation suggest that this huge leap in dimensional enlargement occurred at greater than light speed). The current rate of expansion is specified as one light year per Earth year (think about this and its logic should be revealed).

Note that the units for H are in velocity per specified distance. Thus, the velocity at one million light years is 21.5 km/sec; this means that a galaxy at that distance from Earth is moving away from our planet at that expansion speed. At two million light years it is 2 x 21.5 or 43 km/sec, and so on. If the Universe is indeed 13.7 billion years old, the velocity of the farthest observable galaxies, formed about 13 billion years ago would seem to be 1300 x 21.5 = 27950 km/sec. However, such a calculation is not straightforward since H has varied with time.

Not only has H really changed to other values in the past, its value as determined by astronomers has changed in the last century. In the last 20 years, with the advent of space observatories, the range of values have converged on the presently accepted number. This graph shows this history:

One problem troubling Hubble in the early years after his discovery is that when he used the first value for H he derived to calculate the age of the Universe, it came out around 2+ billion years, a number in stark conflict with the then accepted age of the Earth at about 4 billion years. The contradiction resulted from very imperfect - and too small - estimates of distance to the nearby galaxies he used. As more trustworthy values were obtained, and elliptical galaxies further out were better fixed as to distance, an improved curve resulted (but still applicable to redshift z values [see below] of less than 1). The diagram below is a recent plot of galaxy velocity (in km/sec; converted to kph by multiplying by 3600) versus distance (in megaparsecs) of each galaxy from Earth; the green dots denote specific galaxies for which "reasonably good" measurements have been made (other galaxies have also been so measured but their values are not on this diagram).

Most of these values come from galaxies 5 billion or less light years away. H0 is the present-day Hubble Constant whose precise value is still a major goal in cosmological research; its spread of estimates is related to the uncertainties both in determining the redshift and in fixing the distance of a galaxy at the time light now received left it.

The Hubble Law works best (gives a straight line) from plots of V versus D involving galaxies a few billion or less light years away; uncertainties as to the correctness of distances further out cause an increasing scatter of points in the plot that suggest (or mask) some degree of non-linearity related to the cumulative effects of the curvature of space.

Although called a "constant", H has in fact varied in value over time. In this, it behaves much like the three non-linear plots of R (Scale Factor) versus time shown on the previous page. R describes how distances (as a measured parameter) change over time; H relates distance traveled in a unit time span (usually either Megaparsecs or million years) at each distance moving outward from the point of observation. The two are related. H refers to the relative rate of change of R. The reason that H has different values going back through the past is that it is unlikely that the expansion rate of the Universe has itself been constant since the Big Bang. One model of expansion was strongly influenced by deceleration due to gravitational forces pulling back on the enlarging universe, which means the rate of expansion has been continually decreasing, giving rise to a systematically changing H over the past (its value would increase as we move back in time towards the outer Universe). But now, new evidence for a gradual acceleration about midtime in the Universe's history (see next page) would also affect the variability of H. At best, we can now only determine with reasonable accuracy the value of H0, which proxies for the current value that takes into account the variations in earlier eons of the Universe. We can also say that H was at its maximum value relative to the present right after the extremely large (anomalous) expansion rate of Inflation; we cannot measure this value since we are unable to determine any redshifts until the Universe became transparent.

Hubble was led to the Velocity-Distance Law by interpreting the observed redshifts of stars and galaxies. To appreciate this, we need to explore in more detail what redshifts are.

The concept of "redshift" has been mentioned several times on earlier pages in this Section. Redshift measurements have become the best indicators of cosmic distances - how far away are the stars and galaxies observed through telescopes (see next subsection for a discussion of how these distances are determined). These distances are inputs in calculating the rate of cosmic expansion. There is a systematic relationship between relative velocities of sources of radiation (such as galaxies) as these recede ever faster at increasing distances from Earth and the measured wavelengths of spectral lines from these sources. This is manifested as the redshift - so-called because light from a given wavelength such as in the UV and blue experiences a systematic decrease in frequency (ever longer wavelengths) towards (and beyond) the visible red as expansion velocities increase (this concept is discussed below on this page). As an example, the Lyman Alpha (Hydrogen) spectral line (see page 20-7) normally measured at 1216 Angstroms (in the far UV) when "at rest" on Earth is shifted to 9160 Angstroms (in the near IR) for a galaxy whose redshift is 6.54.

The redshift phenomenon was formalized by V.M. Slipher in 1912 but, in fact, H. Robertson noticed a bit earlier that the farther nearby galaxies were from our telescopes, the greater was the redshift. However, Edwin Hubble in 1924 has received credit for promulgating this redshift-velocity-distance relationship because he included many more galaxies as data points. He thus is recognized as the key individual behind the Expanding Universe model, from whence later came the Big Bang conception of its origin. (Note: Hubble himself never completely accepted the implications of his observations and had doubts about the Big Bang and most of the Universe models described below; for many years after drawing attention to this phenomenon he continued to prefer a Steady State rather than an Expanding Universe, although his position on the latter "mellowed" near the end of his life.) The Hubble Law can be formulated in terms of the redshift value z (where z is the recessional velocity divided by the speed of light; see below) for any celestial object (almost always a galaxy), thusly:

Some of Hubble's observed redshifts led to estimates of galaxy velocities centered around 24 million kph, about 2% the speed of light. Galaxy velocities vary, as indicated in this histogram. Some galaxies can go as fast at 0.1 light speed; a few even faster.